@lanilink,

I believe that this is a bit more of a grey area when it comes to the management of routers, as compared to connecting to the web or another site, as the data is only passing from your device to the router, rather than passing to the web.

For this connection, I believe the only advantage is that you do not get a warning about the connection; the security would come into play when/if your network were to be under attacked and opened to vulnerabilities, as this would encrypt the connections that are passing to your router.

For security purposes, it is recommended that you keep the setting enabled, unless you find a need to disable it. The more layers of security and protection you can place between your device and the internet, the better off you are.

I was also told by one of our QA team that the HTTPS feature may be required by some services if you are looking to access the router interface from outside of your network. Also, if your network is set to only use ipv6, there is a potential for issues accessing the device through one of the methods.